Police are investigating allegations that Pagoda Education Group President Park Kyung-sil plotted to kill a relative of her estranged husband Go In-kyung.

Park is in the process of divorcing Go.

The Seoul Metropolitan Police Agency told The Korea Times, Tuesday, that it may seek an arrest warrant for Park, who has so far rejected summons for questioning.

According to investigators, in August last year Park allegedly paid her driver to kill one of Go's relatives who had frequently advised him on business matters.

However, the driver did not carry out the murder; and he has been questioned by police several times.

Founded in 1969 in Jongno, the Pagoda Academy has grown to become one of the biggest private education companies in Korea. It now runs nine branches nationwide, and in 2012 generated 80 billion won ($74 million) in revenue.

Police searched the headquarters of Pagoda in southern Seoul in February after a tip-off. They did not reveal how much Park paid the driver.

Lee Jung-hwan, Park's lawyer, denied the allegations, claiming that his client gave the driver the money to find and hire a new legal representative for business matters.

"We explained to the police that she would not be immediately available because of the upcoming election for the Korea Association of Hagwon (KAH)," Lee said.

"It also overlaps with the schedule for another legal case."

In this case, police are investigating claims that last year Park gave 1 billion won ($926,354) to a middleman identified as Seo to allegedly bribe officers investigating her for embezzlement and breach of duty.

However, on Jan. 6 she was found guilty of the charges by Seoul Central District Court and sentenced to 18 months in prison suspended for two years.

The focus of the current probe is to figure out whether Seo actually bribed police on her instructions.

Park and Go, the former Pagoda Education Group president, were married in 1979.

Their divorce case has been ongoing since March 2012.

Park has led the Korea Association of Hagwon (private learning institutes), which has more than 50,000 private institutions under its wing, since 2011.

Some of its members held a demonstration Friday, urging her to drop her candidacy for the election today.

According to the laws governing the running of hagwon, people found guilty of criminal acts cannot run such institutions until the terms of their sentences have been completed.